I would say
Artifice / Archaeology / Treasure Hunting (Creates Lightsaber HILTS, which increases a Lightsaber's damage. And CRYSTALS, for different colors, and rare stats you can't find on regular crystals.
Synthweaving / Archaeology / Underworld Goods (Creates Light/Medium/Heavy FORCE USER armor, as well as ENHANCEMENT modifications)
Biochem / Bioanalysis / Diplomacy (Stims, Medpacks, Resuable Medpacks and stims. Implants too)
Cybertech / Scavenging / Underworld Goods (Creates modifications, in the form of Armoring to increase armor raiting, MODS which are used to increase base stats of an item to suit your class, Droid Armor, Ship Armor, and Grenades
All 4 are good choices.
For yourself, Artifice and Biochem would probably be the best options for an Inquisitor in my opinion. (Yourself and 2 or your companions would benefit from the Lightsaber upgrades, and Biochem is just a solid crew skill to have in general)